New Jersey State Police are investigating a claim that Gov. Jon Corzine’s driver was distracted by e-mails from the cop husband of his paramour just before the accident that critically injured the state’s chief executive.

Trooper Robert Rasinski, 34 – already in hot water for speeding at 91 mph and not requiring Corzine to wear a seat belt – now faces accusations he received and read an angry e-mail from his lover’s soon-to-be ex-husband while tearing down the Garden State Parkway on April 13.

David Jones, president of the State Troopers Fraternal Association, said the accusation was made by Sgt. Mike Mathis of the Berkeley Heights Police Department in Union County, N.J. – the jealous husband of Susan Mathis, Rasinski’s girlfriend of more than two years.

“Rob is dating Sue,” Jones said. “I spoke to both of them, and the deal is this is a loveless marriage. At the time Rob met her, she was living in the same house as her husband, but that’s it.”

Jones said divorce papers were filed a few months ago, and the split should be finalized next month. “This guy, Mike Mathis, knew it was over,” Jones said. “So he made a last-ditch effort.”

According to Jones, the effort included Mathis firing Rasinski an e-mail with photos of him and Susan and their children.

Mathis submitted his allegation to police.

The day after the crash, a forum user with the screen name “sqimpm” posted a message on a forum connected to the Newark Star-Ledger’s Web site hinting Rasinski may have been distracted.

“I would like to know if Trooper Rasinski had a Blackberry-type cellphone at the time of the accident,” it read. “I wonder if he could have been reading any e-mail causing him to be inattentive at the time of the accident. I think that would be worth looking into.”

The message was signed “Mike Mathis.”

Yesterday, a user with the same screen name again claimed to be the cuckolded cop.

“I am the soon to be ex-husband,” the user wrote. “I want to let you know that the divorce process only started a month ago after learning about a 2½ year long affair Rasinski was having with my wife.”

“My problem is not with the NJ State Police,” he wrote. “My problem is with Rasinski.”

Mathis was unavailable for comment yesterday.

Union boss Jones dismissed the distraction allegation.

“There is absolutely no truth to these claims whatsoever,” Jones said.

Rasinski didn’t open the e-mail until after the accident, Jones said.

“Rob doesn’t even have a Blackberry,” Jones said.

Rasinski and Susan Mathis were unavailable for comment. Calls to Corzine’s office for comment were not returned.

Corzine remained in critical but stable condition at Cooper University Hospital and showed signs of recovery yesterday.